What is the use of the regular convolutional layer in expansion path of U-Net?
The point is that in the expansive path you have two forms of information:

the information from the contracting path, which includes all high-level features extracted from the original image.
the information from the skip-connections, which copy a cropped version of the feature maps in the contracting path. Because, as we go forward through the expansive path these originate from earlier stages in the contracting path, these are progressively richer in detail.

Intuitively you can think of it as this: high-level features help the network tell which areas to group together, while details help it tell where each group starts and ends at the pixel level.
The idea is to combine these two forms of information, i.e. the high-level features and the details, optimally.  To do this you need trainable layers that learn this optimal combination. Here is where the convolution layers come to play.